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First Steps in Linear Algebra for Machine Learning
Week 3
Week 3

- Video: LectureCoordinates and basis
  . Duration: 12 minutes
- Video: LectureCoordinates change example
  . Duration: 9 minutes
- Quiz: Week 3
  11 questions

QuizQuiz • 30 min30 minutes

Week 3

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Week 3

Graded Quiz • 30 min

Due Jun 1, 2:59 AM EDT

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To Pass 100% or higher

Grade

100%

Week 3

Latest Submission Grade

100%

1.

Question 1

What properties does a subset of a vector space L have to have in order to be a subspace:

1 / 1 point

Correct

2.

Question 2

Find the length of $x=$

(1 - 7 3)

x = (1 - 7 3)

.

x

is a vector in Euclidean space.

1 / 1 point

Correct

3.

Question 3

Find the angle between x and y, if $x=$

(1 - 3 0)

^T, y=

(01 - 7)

^T

x = (1 - 3 0)^{T}, y = (01 - 7)^{T}

x, y are vectors in Euclidean space.

1 / 1 point

Correct

4.

Question 4

Find the dot product $\left\langle x,y \right\rangle$ if $x=$

⎛ ⎝ ⎜ ⎜ 9 - 2 4 ⎞ ⎠ ⎟ ⎟

x = ⎝ ⎜ ⎛ 9 - 2 4 ⎠ ⎟ ⎞

and

y=

x, y

\in \mathcal{E}

.

1 / 1 point

Correct

5.

Question 5

Given a new basis $E'=\left\lbrace e'_1=i+k, e'_2=-i-j, e'_3=3k-i \right\rbrace$ , find $x=5i-7j+8k$ in E'. $i,j,k$ is the standart basis.

1 / 1 point

Correct

6.

Question 6

Suppose $\left\lbrace a_1=$

⎛ ⎝ ⎜ ⎜ 101 ⎞ ⎠ ⎟ ⎟

, a_2=

⎛ ⎝ ⎜ ⎜ 0 - 1 1 ⎞ ⎠ ⎟ ⎟

\right\rbrace

⎩ ⎪ ⎨ ⎪ ⎧ a_{1} = ⎝ ⎜ ⎛ 101 ⎠ ⎟ ⎞, a_{2} = ⎝ ⎜ ⎛ 0 - 1 1 ⎠ ⎟ ⎞ ⎭ ⎪ ⎬ ⎪ ⎫

is a basis in

L\subset\mathcal{E}

and

x=

Find

pr_Lx

.

1 / 1 point

Correct

7.

Question 7

Find the approximation to the solution of $Ax=b$ , where $A=$

⎛ ⎝ ⎜ ⎜ 310 - 5 - 7 1 ⎞ ⎠ ⎟ ⎟

A = ⎝ ⎜ ⎛ 310 - 5 - 7 1 ⎠ ⎟ ⎞

and

b=

. Use least squares method.

1 / 1 point

Correct